Figure 2The Production Function The production function is the relationship

# Figure 2the production function the production

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Figure 2The Production Function The production function is the relationship between the inputs into production (apple pickers) and the output from production (apples). As the quantity of the input increases, the production function gets flatter, reflecting the property of diminishing marginal product. 18-1C The Value Of The Marginal Product And The Demand For Labor Our profit-maximizing firm is concerned more with money than with apples. As a result, when deciding how many workers to hire to pick apples, the firm considers how much profit each worker would bring in. Because profit is total revenue minus total cost, the profit from an additional worker is the worker's contribution to revenue minus the worker's wage. To find the worker's contribution to revenue, we must convert the marginal product of labor (which is measured in bushels of apples) into the value of the marginal product (which is measured in dollars). We do this using the price of apples. To continue our example, if a bushel of apples sells for \$10 and if an additional worker produces 80 bushels of apples, then the worker produces \$800 of revenue. The value of the marginal product of any input is the marginal product of that input multiplied by the market price of the output. The fourth column in Table shows the value of the marginal product of labor in our example, assuming the price of apples is \$10 per bushel. Because the market price is constant for a competitive firm while the marginal product declines with more workers, the value of the marginal product diminishes as the number of workers rises. Economists sometimes call this column of numbers the firm's marginal revenue product: It is the extra revenue the firm gets from hiring an additional unit of a factor of production. Now consider how many workers the firm will hire. Suppose that the market wage for apple pickers is \$500 per week. In this case, as you can see in Table 1, the first worker that the firm hires is profitable: The first worker yields \$1,000 in revenue, or \$500 in profit. Similarly, the
second worker yields \$800 in additional revenue, or \$300 in profit. The third worker produces \$600 in additional revenue, or \$100 in profit. After the third worker, however, hiring workers is unprofitable. The fourth worker would yield only \$400 of additional revenue. Because the worker's wage is \$500, hiring the fourth worker would mean a \$100 reduction in profit. Thus, the firm hires only 3 workers. It is instructive to consider the firm's decision graphically. Figure 3 graphs the value of the marginal product. This curve slopes downward because the marginal product of labor diminishes as the number of workers rises. The figure also includes a horizontal line at the market wage. To maximize profit, the firm hires workers up to the point where these two curves cross. Below this level of employment, the value of the marginal product exceeds the wage, so hiring another worker would increase profit. Above this level of employment, the value of the marginal product is less than the wage, so the marginal worker is unprofitable. Thus,

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